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Author Archives: aldenwalker
Hyperbolic Geometry Notes #5 – Mostow Rigidity
1. Mostow Rigidity For hyperbolic surfaces, Moduli space is quite large and complicated. However, in three dimensions Moduli space is trivial: Theorem 1 If is a homotopy equivalence of closed hyperbolic manifolds with , then is homotopic to an isometry. … Continue reading
Posted in 3manifolds, Groups, Hyperbolic geometry, Uncategorized
3 Comments
Hyperbolic Geometry Notes #4 – FenchelNielsen Coordinates
1. FenchelNielsen Coordinates for Teichmuller Space Here we discuss a very nice set of coordinates for Teichmuller space. The basic idea is that we cut the surface up into small pieces (pairs of pants); hyperbolic structures on these pieces are … Continue reading
Posted in Hyperbolic geometry
4 Comments
Hyperbolic Geometry Notes #3 – Teichmuller and Moduli Space
This post introduces Teichmuller and Moduli space. The upcoming posts will talk about FenchelNielsen coordinates for Teichmuller space; it’s split up because I figured this was a relatively nice break point. Hopefully, I will later add some pictures to this … Continue reading
Posted in Hyperbolic geometry
3 Comments
Hyperbolic Geometry Notes #2 – Triangles and Gauss Bonnet
In this post, I will cover triangles and area in spaces of constant (nonzero) curvature. We are focused on hyperbolic space, but we will talk about spheres and the GaussBonnet theorem. 1. Triangles in Hyperbolic Space Suppose we are given … Continue reading
Hyperbolic Geometry (157b) Notes #1
I am Alden, one of Danny’s students. Error/naivete that may (will) be found here is mine. In these posts, I will attempt to give notes from Danny’s class on hyperbolic geometry (157b). This first post covers some models for hyperbolic … Continue reading →